SOLUTION: A hiker travels up a mountain path and then back down again. The total time for the trip was 8.00 hours. The hiker traveled 2.00 mph faster on the way down than on the way up. What

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A hiker travels up a mountain path and then back down again. The total time for the trip was 8.00 hours. The hiker traveled 2.00 mph faster on the way down than on the way up. What      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1153492: A hiker travels up a mountain path and then back down again. The total time for the trip was 8.00 hours. The hiker traveled 2.00 mph faster on the way down than on the way up. What was the total length of the hike, if the rate up the mountain was 2.90.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Same distance d up and down

              SPEED          TIME      DISTANCE

UP             2.90           d/2.9      d

DOWN           4.90           d/4.9      d

TOTAL                         8

The question asks for 2d.

highlight_green%28d%2F2.9%2Bd%2F4.9=8%29

4.9d%2B2.9d=8%2A4.9%2A2.9
7.8d=8%2A4.9%2A2.9
d=%288%2A4.9%2A2.9%29%2F7.8
highlight%282d=2%28%288%2A4.9%2A2.9%29%2F7.8%29%29------compute this.


29.1 miles, total trip

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Here is an alternative method for solving problems like this that I personally find gets me to the answer faster than the formal algebraic solution suggested by the other tutor.

The distances up and back are the same; the ratio of the two speeds is 2.90:4.90 = 29:49.

That means the fraction of the total time spent going up the mountain was 49/(29+49) = 49/78.

So the number of hours spent going up the mountain was

%2849%2F78%29%2A8+=+392%2F78+=+196%2F39

And then the distance up the mountain is rate times time:

%28196%2F39%29%2A2.9 = 14.574 miles, to 3 decimal places.

Assuming, then, that "total length of the hike" means both directions, the total length was about 29.15 miles.